scholarly journals Attributable risk function in the proportional hazards model for censored time-to-event

Biostatistics ◽  
2006 ◽  
Vol 7 (4) ◽  
pp. 515-529 ◽  
Author(s):  
Y. Q. Chen
Keyword(s):  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Risk Function ◽  
Attributable Risk ◽  
Time To Event ◽  
Hazards Model

scholarly journals A tutorial on frailty models

2020 ◽  
Vol 29 (11) ◽  
pp. 3424-3454 ◽  
Author(s):  
Theodor A Balan ◽  
Hein Putter
Keyword(s):  
Random Effects ◽  
Recurrent Events ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Unobserved Heterogeneity ◽  
Frailty Models ◽  
Survival Outcomes ◽  
Time To Event ◽  
Homogeneous Population ◽  
Hazards Model

The hazard function plays a central role in survival analysis. In a homogeneous population, the distribution of the time to event, described by the hazard, is the same for each individual. Heterogeneity in the distributions can be accounted for by including covariates in a model for the hazard, for instance a proportional hazards model. In this model, individuals with the same value of the covariates will have the same distribution. It is natural to think that not all covariates that are thought to influence the distribution of the survival outcome are included in the model. This implies that there is unobserved heterogeneity; individuals with the same value of the covariates may have different distributions. One way of accounting for this unobserved heterogeneity is to include random effects in the model. In the context of hazard models for time to event outcomes, such random effects are called frailties, and the resulting models are called frailty models. In this tutorial, we study frailty models for survival outcomes. We illustrate how frailties induce selection of healthier individuals among survivors, and show how shared frailties can be used to model positively dependent survival outcomes in clustered data. The Laplace transform of the frailty distribution plays a central role in relating the hazards, conditional on the frailty, to hazards and survival functions observed in a population. Available software, mainly in R, will be discussed, and the use of frailty models is illustrated in two different applications, one on center effects and the other on recurrent events.

A censored quantile regression approach for the analysis of time to event data

2016 ◽  
Vol 27 (3) ◽  
pp. 955-965 ◽  
Author(s):  
Xiaonan Xue ◽  
Xianhong Xie ◽  
Howard D Strickler
Keyword(s):  
Quantile Regression ◽  
Regression Model ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Cox Proportional Hazards ◽  
Cox Proportional Hazards Model ◽  
Time To Event ◽  
Censored Quantile Regression ◽  
Quantile Regression Model ◽  
Hazards Model

The commonly used statistical model for studying time to event data, the Cox proportional hazards model, is limited by the assumption of a constant hazard ratio over time (i.e., proportionality), and the fact that it models the hazard rate rather than the survival time directly. The censored quantile regression model, defined on the quantiles of time to event, provides an alternative that is more flexible and interpretable. However, the censored quantile regression model has not been widely adopted in clinical research, due to the complexity involved in interpreting its results properly and consequently the difficulty to appreciate its advantages over the Cox proportional hazards model, as well as the absence of adequate validation procedure. In this paper, we addressed these limitations by (1) using both simulated examples and data from National Wilms’ Tumor clinical trials to illustrate proper interpretation of the censored quantile regression model and the differences and the advantages of the model compared to the Cox proportional hazards model; and (2) developing a validation procedure for the predictive censored quantile regression model. The performance of this procedure was examined using simulation studies. Overall, we recommend the use of censored quantile regression model, which permits a more sensitive analysis of time to event data together with the Cox proportional hazards model.

scholarly journals A new modeling and inference approach for the Systolic Blood Pressure Intervention Trial outcomes

2018 ◽  
Vol 15 (3) ◽  
pp. 305-312 ◽  
Author(s):  
Song Yang ◽  
Walter T Ambrosius ◽  
Lawrence J Fine ◽  
Adam P Bress ◽  
William C Cushman ◽  
...  
Keyword(s):  
Treatment Effect ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Rank Test ◽  
Time To Event ◽  
New Approach ◽  
New Methods ◽  
Log Rank Test ◽  
Hazards Model ◽  
Average Hazard Ratio

Background/aims In clinical trials with time-to-event outcomes, usually the significance tests and confidence intervals are based on a proportional hazards model. Thus, the temporal pattern of the treatment effect is not directly considered. This could be problematic if the proportional hazards assumption is violated, as such violation could impact both interim and final estimates of the treatment effect. Methods We describe the application of inference procedures developed recently in the literature for time-to-event outcomes when the treatment effect may or may not be time-dependent. The inference procedures are based on a new model which contains the proportional hazards model as a sub-model. The temporal pattern of the treatment effect can then be expressed and displayed. The average hazard ratio is used as the summary measure of the treatment effect. The test of the null hypothesis uses adaptive weights that often lead to improvement in power over the log-rank test. Results Without needing to assume proportional hazards, the new approach yields results consistent with previously published findings in the Systolic Blood Pressure Intervention Trial. It provides a visual display of the time course of the treatment effect. At four of the five scheduled interim looks, the new approach yields smaller p values than the log-rank test. The average hazard ratio and its confidence interval indicates a treatment effect nearly a year earlier than a restricted mean survival time–based approach. Conclusion When the hazards are proportional between the comparison groups, the new methods yield results very close to the traditional approaches. When the proportional hazards assumption is violated, the new methods continue to be applicable and can potentially be more sensitive to departure from the null hypothesis.

scholarly journals A family of partial-linear single-index models for analyzing complex environmental exposures with continuous, categorical, time-to-event, and longitudinal health outcomes

2020 ◽  
Author(s):  
Yuyan Wang ◽  
Yinxiang Wu ◽  
Melanie H. Jacobson ◽  
Myeonggyun Lee ◽  
Peng Jin ◽  
...  
Keyword(s):  
Environmental Factors ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Nonlinear Effects ◽  
Parametric Models ◽  
Time To Event ◽  
Joint Effects ◽  
Single Index ◽  
Hazards Model ◽  
Partial Linear

Abstract Background: Statistical methods to study the joint effects of environmental factors are of great importance to understand the impact of correlated exposures that may act synergistically or antagonistically on health outcomes. This study proposes a family of statistical models under a unified partial-linear single-index (PLSI) modeling framework, to assess the joint effects of environmental factors for continuous, categorical, time-to-event, and longitudinal outcomes. All PLSI models consist of a linear combination of exposures into a single index for practical interpretability of relative direction and importance, and a nonparametric link function for modeling flexibility. Methods: We presented PLSI linear regression and PLSI quantile regression for continuous outcome, PLSI generalized linear regression for categorical outcome, PLSI proportional hazards model for time-to-event outcome, and PLSI mixed-effects model for longitudinal outcome. These models were demonstrated using a dataset of 800 subjects from NHANES 2003-2004 survey including 8 environmental factors. Serum triglyceride concentration was analyzed as a continuous outcome and then dichotomized as a binary outcome. Simulations were conducted to demonstrate the PLSI proportional hazards model and PLSI mixed-effects model. The performance of PLSI models was compared with their counterpart parametric models. Results: PLSI linear, quantile, and logistic regressions showed similar results that the 8 environmental factors had both positive and negative associations with triglycerides, with a-Tocopherol having the most positive and trans-b-carotene the most negative association. For the time-to-event and longitudinal settings, simulations showed that PLSI models could correctly identify directions and relative importance for the 8 environmental factors. Compared with parametric models, PLSI models got similar results when the link function was close to linear, but clearly outperformed in simulations with nonlinear effects. Conclusions: We presented a unified family of PLSI models to assess the joint effects of exposures on four commonly-used types of outcomes in environmental research, and demonstrated their modeling flexibility and effectiveness, especially for studying environmental factors with mixed directional effects and/or nonlinear effects. Our study has expanded the analytical toolbox for investigating the complex effects of environmental factors. A practical contribution also included a coherent algorithm for all proposed PLSI models with R codes available.

scholarly journals Estimating Proportional Hazards Model Using Frequentist and Bayesian Approaches

2014 ◽  
Vol 8 (2) ◽  
Author(s):  
Noraslinda Mohamed Ismail ◽  
Zarina Mohd Khalid ◽  
Norhaiza Ahmad
Keyword(s):  
Bayesian Approach ◽  
Survival Data ◽  
Hazard Function ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Risk Function ◽  
Model Parameters ◽  
Right Censored Data ◽  
Hazards Model ◽  
Leukemia Data

In statistics, the proportional hazards model (PHM) is one of a class of survival models. This model estimates the effects of different covariates influencing the time-to-event data in which the hazard function has been assumed to be the product of the baseline hazard function and a non-negative function of covariates. In this study, we investigate the hazard function, also known as the risk function or intensity function, which is employed in modelling the survival data and waiting times. The model parameters can be estimated via frequentist or Bayesian approach. However, the Bayesian approach is well known to have the advantages over frequentist methods when the data are small in size and involve censored individuals. In this paper, the PHM for right-censored data from Bayesian perspective will be discussed and the Markov Chain Monte Carlo (MCMC) method will be used to estimate the posterior distributions of the model parameters using Leukemia data.

scholarly journals A family of partial-linear single-index models for analyzing complex environmental exposures with continuous, categorical, time-to-event, and longitudinal health outcomes

2020 ◽  
Author(s):  
Yuyan Wang ◽  
Yinxiang Wu ◽  
Melanie Jacobson ◽  
Myeonggyun Lee ◽  
Peng Jin ◽  
...  
Keyword(s):  
Environmental Factors ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Nonlinear Effects ◽  
Parametric Models ◽  
Time To Event ◽  
Joint Effects ◽  
Single Index ◽  
Hazards Model ◽  
Partial Linear

Abstract Background: Statistical methods to study the joint effects of environmental factors are of great importance to understand the impact of correlated exposures that may act synergistically or antagonistically on health outcomes. This study proposes a family of statistical models under a unified partial-linear single-index (PLSI) modeling framework, to assess the joint effects of environmental factors for continuous, categorical, time-to-event, and longitudinal outcomes. All PLSI models consist of a linear combination of exposure factors into a single index for practical interpretability of relative direction and importance, and a nonparametric link function for modeling flexibility. Methods: We presented PLSI linear regression and PLSI quantile regression for continuous outcome, PLSI generalized linear regression for categorical outcome, PLSI proportional hazards model for time-to-event outcome, and PLSI mixed-effects model for longitudinal outcome. These models were demonstrated using a dataset of 800 subjects from NHANES 2003-2004 survey including 8 environmental factors. Serum triglyceride concentration was analyzed as a continuous outcome and then dichotomized as a binary outcome. Simulations were conducted to demonstrate the PLSI proportional hazards model and PLSI mixed-effects model. The performance of PLSI models was compared with their counterpart parametric models. Results: PLSI linear, quantile, and logistic regressions showed similar results that the 8 environmental factors had both positive and negative associations with triglycerides, with a-Tocopherol having the most positive and trans-b-carotene the most negative association. For the time-to-event and longitudinal settings, simulations showed that PLSI models could correctly identify directions and relative importance for the 8 environmental factors. Compared with parametric models, PLSI models got similar results when the link function was close to linear, but clearly outperformed in simulations with nonlinear effects. Conclusions: We presented a unified family of PLSI models to assess the joint effects of exposures on four commonly-used types of outcomes in environmental research, and demonstrated their modeling flexibility and effectiveness, especially for studying environmental factors with mixed directional effects and/or nonlinear effects. Our study has expanded the analytical toolbox for investigating the complex effects of environmental factors. A practical contribution also included a coherent algorithm for all proposed PLSI models with R codes available.

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